The novel coronavirus (SARS-CoV-2) pandemic that started in late 2019 is responsible for hundreds of millions of cases worldwide and millions of fatalities. Though vaccines are available, the virus is mutating to form new strains among which are the variants B.1.1.7 and B.1.351 that demonstrate increased transmissivity and infectivity. In this study, we performed molecular dynamics simulations to explore the role of the mutations in the interaction of the virus spike protein receptor binding domain (RBD) with the host receptor ACE2. We find that the hydrogen bond networks are rearranged in the variants and also that new hydrogen bonds are established between the RBD and ACE2 as a result of mutations. We investigated three variants: the wild-type (WT), B.1.1.7, and B.1.351. We find that the B.1.351 variant (also known as 501Y.V2) shows larger flexibility in the RBD loop segment involving residue K484, yet the RBD-ACE2 complex shows higher stability. Mutations that allow a more flexible interface that can result in a more stable complex may be a factor contributing to the increased infectivity of the mutated variants.